Existence and uniqueness of the solution of the initial value problem for the Boltzmann transport equation in an indefinite homogeneous multiplicative medium are proved. Moreover, the existence of at least one real eigenvalue of the transport operator is displayed. Finally, the asymptotic behavior of the neutron density is indicated as t → + ∞.
The formalism of the reproducing kernel method is used to evaluate exponents of bounded operators. Reproducing kernels are built with interpolating properties that do take into account any approximate knowledge of the spectrum. The explicit solution of linear evolution equations is reduced to the solution of a few static problems.
Neutron capture radiative cross sections for Ta, Ag, In and Au have been measured between 30 keV and 1·5 MeV using time-of-flight technique. The detector used was a large liquid scintillator. Cross-sections are given in relative and absolute units.
The method of reproducing kernels developed in the first part is used to solve a time dependent thermalization problem. The time dependence associated with the continuous spectrum is given explicitly.
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